extreme f(x)=x^6-3x^4

Lösung

extrempunkte

f (x) = x^{6} - 3 x^{4}

Minimum (- 2, - 4), Maximum (0, 0), Minimum (2, - 4)

Schritte zur Lösung

f^{'} (x) = 6 x^{5} - 12 x^{3}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

x^{6} - 3 x^{4} : - 4

Minimum (- 2, - 4)

Stecke

x = 0

x^{6} - 3 x^{4} : 0

Maximum (0, 0)

Stecke

x = 2

x^{6} - 3 x^{4} : - 4

Minimum (2, - 4)

Minimum (- 2, - 4), Maximum (0, 0), Minimum (2, - 4)

e x t re m e f (x, y) = x^{2} + 3 x y + 4 y^{2} - 6 x + 2 y

e x t re m e f (x) = 250 + 8 x^{3} + x^{4}

e x t re m e f (x, y) = \frac{x + 4}{y ^{2} - x ^{2}}

e x t re m e f (x, y) = (x - 1)^{2} + y^{3} - 3 y^{2} - 9 y + 5

e x t re m e f (x) = 3 cos (3 x) + sin (3 x)